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isomorphism -- retrieve an isomorphism of modules

Description

This method retrieves the isomorphism between the given modules. Note that this isomorphism is already cached if a previous call to isIsomorphic returned true, but otherwise that function is called.

i1 : S = ZZ/32003[x_0..x_3]

o1 = S

o1 : PolynomialRing
i2 : m = random(S^3, S^{4:-2});

             3      4
o2 : Matrix S  <-- S
i3 : A = random(target m, target m);

             3      3
o3 : Matrix S  <-- S
i4 : B = random(source m, source m);

             4      4
o4 : Matrix S  <-- S
i5 : N = coker(A*m*B);
i6 : M = coker m;
i7 : f = isomorphism(N, M)

o7 = | 1     4078 4892  |
     | -2922 6959 -89   |
     | -5122 -889 -1064 |

o7 : Matrix N <-- M
i8 : isIsomorphism f

o8 = true

See also

Ways to use isomorphism:

  • isomorphism(Module,Module)

For the programmer

The object isomorphism is a method function with options.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/Isomorphism.m2:528:0.